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The topology optimization as a part of the structural optimization helps engineers to design products or single parts to meet the contrived requirements in an optimal way. This can be maximum stiffness with low volume or maximum stability with low mass. Thereby great possible savings can be achived in terms of less application of energy in production, less material usage and less workload in development. These benefits facilitate a kind of construction and production which meets the principle of sustainabilty.
For best use of these possible savings, the topology optimization is applied in the early concept phase of the product development process. Here a great freedom in design exists, which later on has a great influence on the upcoming costs. At the same time the costs for modifications are pretty low.
The effort for a topology optimization is fairly humble. At first the operator defines the available design space for the considered part. Then the location and amount of strain as well as regions in which the part’s shape should not be altered – i. e. drilling holes – are specified. After that an optimization run can be started and the optimization software does the rest.
Depending on the used method and the pursued target, the optimization software gains the required data for processing from a Finite-Element-Analysis (FEA). Among other things, this can be displacements or the part’s stress.
With the help of the FEA data, the structure of the part is altered by variation of the Young’s Modulus of the finite elements. In the process a low Young’s Modulus represents a hole and a high Young’s Modulus describes a solid element. With this new distribution a FEA is performed in the next iteration, at which an element with a low Young’s Modulus shows a fairly flexible behaviour and does not – like a hole – contribute to the stiffness of the structure. At some methods the Young’s Modulus is indirectly determined through another parameter. All variables which are customized by the optimization algorithm are called design variables.
How the Young’s Modulus is modified depends on the used method. The existing techniques can be roughly subclassified in mathematical and empirical methods. For the mathematical optimization the design variables are varied based on a mathematically derived principle leading to optimality. On the other hand, empirical methods change the design variables based on a rule which assumes optimality and generally generate a good result in a short amount of time. Z88Arion® uses methods from both groups.

In the 50s, the linear finite element method was the starting point for the success story of FEM calculations in praxis.

With this type of calculation, it is assumed that the results are proportional to the loads. Through this assumption the solution of the problem becomes much easier.

Nevertheless, this method has not served out yet. Most of daily life objects deform linear elastic in certain ranges. Therefore the linear FEM is the easiest and fastest method to conduct calculations. It gives important information on component strength and possible weaknesses to the designer.

With Z88Aurora® V2 the possibility to  carry out non-linear simulations was introduced. Included are geometric non-linearities as a result of big displacements. This type of non-linearity occurs when drastic changes in the model geometry are caused by the structure’s deformation. Heavily deformed structures have a very high chance of displaying a stiffness behaviour with geometric non-linearities. This is why a non-linear solver should be used to calculate such structures to avoid huge  errors concerning the calculated displacements, forces and stresses.

The possibility to simulate material non-linearities was introduced in Z88Aurora® V3. They are a result of high stresses/strains and can be taken into account by providing the solver with addidtional material data, e.g. a stress over strain curve. This gives Z88Aurora® V3 the  capability to simulate plastic material behaviour, non-elastic deformations and spring-back effects. Furthermore the calculation of stresses is much more accurate for high loads. Also included is the possibility to calculate internal stresses, that result from a plastic deformation.

Z88Aurora® offers an iterative solver for non-linear calculations. Features include:

• Supported element types for geometric non-linearities
  • Hexahedron No. 1 (linear) & No. 10 (quadratic)
  • Tetrahedron No. 16 (quadratic) & No. 17 (linear)
  • Plane stress element No. 7 and Torus No. 8
  • Truss 3D No. 4
• Supported element types for plasticity
  • Hexahedron No. 1 (linear)
  • Tetrahedron No. 16 (quadratic)
• Elastic-plastic material models:
  • von Mises
  • Wehmann & modified Wehmann
• Spring-back analysis optional with varying number of steps
• Results for each load step

Z88V14OS does not offer non-linear analysis options.

Many properties of components are temperature dependent and have to be investigated during their development.

With the help of steady state thermal finite element method designers and engineers are able to perform analysis of the thermal behavior of their product within each design phase. Due to a coupling of thermal and mechanical boundary conditions, it is possible to compute thermal results, such as temperature or heat flux, as well as thermal-mechanical displacements or stresses. This ensures that part temperatures during operation are within allowed limits. Possibly upcoming security issues can be examined and eliminated in an early phase of the product development process.

Z88Aurora® uses three numerical solvers for steady state thermal and thermal-mechanical simulations respectively:

• Two different preconditioned iterative solvers with sparse storage for big finite element structures

• One direct Multicore-solver (PARDISO) with sparse storage for medium-sized finite element structures
• Available element types for thermal simulations:
  • Hexahedron No. 1 (linear) & No. 10 (quadratic)
  • Tetrahedron No. 16 (quadratic) & No. 17 (linear)

Unfortunately it is not possible to perform thermal analyses by Z88V14OS.